Finite Model Theory

Finite Model Theory (FMT) is a subarea of Model Theory (MT). MT is the branch of mathematical logic which deals with the relation between a formal language (syntax) and its interpretations (semantics). FMT is a restriction of MT to finite structures, such as finite graphs or strings. Since many central theorems of MT do not hold when restricted to finite structures, FMT is quite different from MT in methods and application areas. FMT has become an "unusually effective" instrument in computer science, for example in database theory, model checking or for gaining new perspectives on computational complexity.

The three main areas of FMT are presented here: Expressive Power of Languages, Descriptive Complexity, and Random Structures. But first the results fundamental for all areas are introduced on the level of first order languages.